The value of ^ -1 ( ( 2 ) )+ ^ -1 ( (2 3 ) ) is - Vidyadip

MCQ

The value of $\cos ^{-1}\left(\cot \left(\frac{\pi}{2}\right)\right)+\cos ^{-1}\left(\sin \left(\frac{2 \pi}{3}\right)\right)$ is

✓
$\frac{2 \pi}{3}$
B
$\frac{\pi}{3}$
C
$\frac{\pi}{2}$
D
$\pi$

✓

Answer

Correct option: A.

$\frac{2 \pi}{3}$

(a) : $\cos ^{-1}\left(\cot \frac{\pi}{2}\right)+\cos ^{-1}\left(\sin \frac{2 \pi}{3}\right)$
$=\cos ^{-1}(0)+\cos ^{-1}\left(\frac{\sqrt{3}}{2}\right)$
$=\frac{\pi}{2}+\cos ^{-1}\left(\cos \frac{\pi}{6}\right)=\frac{\pi}{2}+\frac{\pi}{6}=\frac{4 \pi}{6}=\frac{2 \pi}{3}$

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